Next let A, BC not be prime to one another;
then BC either measures, or does not measure, A.
If now BC measures A, BC is a part of A.
But, if not, let the greatest common measure D of A, BC be taken; [VII. 2]
and let BC be divided into the numbers equal to D, namely BE, EF, FC.
Now, since D measures A, D is a part of A.
But D is equal to each of the numbers BE, EF, FC;
therefore each of the numbers BE, EF, FC is also a part of A;
so that BC is parts of A.